New family of error-correcting codes based on genetic algorithms

Abstract

This paper introduces a novel error-correcting code (ECC) construction and decoding approach utilizing genetic algorithms (GAs). Classical ECCs often struggle with efficiency in correcting multiple errors due to time-consuming matrix-based encoding and decoding processes. Our GA-based method optimizes generator vectors to maximize the minimum distance between codewords, enhancing error correction capabilities. Specifically, we construct a new family of ECCs with code length 31, dimension 12, and minimum distance 7, reducing complexity from O(kn) to O(k(n−k)) by encoding message blocks with vectors instead of matrices. In the decoding phase, the GA effectively corrects errors in received codewords. Experimental results show that at a signal-to-noise ratio (SNR) of 7.7 dB, our method achieves a bit error rate (BER) of 10−5 after only 9 generations of the GA. These results demonstrate improved error correction and decoding performance compared to traditional methods. This study contributes an innovative approach using GAs for error correction, offering simpler encoding and robust performance in coding schemes.